The isentropic quantum drift-diffusion model in two or three space dimensions

DOI10.1007/S00033-008-7068-4zbMath1173.35518OpenAlexW1993069012MaRDI QIDQ834547

Xiu-Qing Chen

Publication date: 27 August 2009

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-008-7068-4

zbMATH Keywords

weak solutionperiodic boundary conditionssemiclassical limitcompactness argumentinterpolation estimatesquantum drift-diffusionfourth order parabolic system

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with optics and electromagnetic theory (35Q60) Initial-boundary value problems for higher-order parabolic equations (35K35) Nonlinear elliptic equations (35J60) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (4)

Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors. ⋮ On the effects of the Bohm potential on a macroscopic system of self-interacting particles ⋮ Existence and semiclassical limit for the quantum drift-diffusion model ⋮ A sixth-order parabolic system in semiconductors

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